Evaluate (-125)^(-2/3)

Problem

(−125)(−2/3)

Solution

1. Apply the negative exponent rule to rewrite the expression as a reciprocal with a positive exponent.

1/((−125)(2/3))

2. Interpret the fractional exponent as a power of a root, specifically the square of the cube root.

1/((√(3,−125))2)

3. Evaluate the cube root of −125 noting that (−5)×(−5)×(−5)=−125

1/((−5)2)

4. Square the result to find the final value.

1/25

Final Answer

(−125)(−2/3)=1/25

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